https://file.aiquickdraw.com/mathbot/file/1729259878512ydqcrwzf.jpg

The problem in your image is asking for a proof that \( WY \cong WX \) using congruent triangles. Let's break down the steps in the proof from the given image:

### Given Information:
1. \( \angle Y \cong \angle X \) (Given)
2. \( XY \cong XY \) (Reflexive Property of Congruence)

### Completing the Proof:
3. **\( \triangle WXY \cong \triangle WYX \)** by the **Angle-Side-Angle (ASA)** Congruence Postulate.  
   - Reason: The triangles share the side \( XY \) (which is congruent to itself by the Reflexive Property), and both triangles have two congruent angles: \( \angle Y \cong \angle X \) (given) and the included angle at vertex \( W \), \( \angle WXY \cong \angle WYX \), since they are opposite angles in the two triangles.

4. **\( WY \cong WX \)** because corresponding parts of congruent triangles are congruent (CPCTC).

### Complete Statement Table:

| Statement                          | Reason                                     |
|-------------------------------------|--------------------------------------------|
| 1. \( \angle Y \cong \angle X \)    | Given                                      |
| 2. \( XY \cong XY \)                | Reflexive Property of Congruence            |
| 3. \( \triangle WXY \cong \triangle WYX \) | Angle-Side-Angle (ASA) Postulate       |
| 4. \( WY \cong WX \)                | Corresponding Parts of Congruent Triangles (CPCTC) |

This proof shows that \( WY \) is congruent to \( WX \) as corresponding sides of the congruent triangles \( WXY \) and \( WYX \).

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Would you like any further explanation on any of the steps in this proof, or do you have any other questions?

Here are 5 follow-up questions to consider:
1. How does the Reflexive Property of Congruence work in proofs?
2. What other congruence postulates could be used if given different information?
3. Why is it important to prove two triangles are congruent in geometric proofs?
4. What are some common mistakes when using the CPCTC rule?
5. How can you use Angle-Side-Angle (ASA) in real-world applications?

**Tip:** When solving triangle congruence problems, always check if you have enough information to apply one of the triangle congruence postulates (like ASA, SSS, or SAS).

Complete the proof that WY ≅ WX given that ∠Y ≅ ∠X, and using the properties of congruent triangles.

Learn how to prove that WY is congruent to WX by using the Angle-Side-Angle (ASA) Postulate and CPCTC in this geometry problem. The proof involves congruent triangles, the reflexive property, and corresponding parts of congruent triangles. Suitable for high school students in grades 9-11.

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